Underdetermination: Duhem, Laudan

Two criticisms of conventional views about the relation between
theory and evidence from the Duhem selection:

Holism. (Laudan calls this "the ambiguity of
falsification" on p. 326.) This is the idea that evidence does not bear directly on a
hypothesis alone, but rather on a hypothesis in conjunction with many additional
theoretical claims (as well as assumptions about particular facts, e.g. about the
experimental setup).

Let H be the hypothesis we wish to test; let A1, A2, and A3
be the additional theoretical and particular assumptions needed to deductively imply an
observation statement, and let O be the observation statement.

Then we may think of Duhem as making the following point. If H, together with A1,
A2, and A3, implies O, then the following conditional will be true:

(H & A1
& A2 & A3)
→O

From this, together with ~O, we can deduce, not ~H, but only

~(H & A1
& A2 & A3)

Which (by DeMorgan's laws) is equivalent to

~H
∨~A1∨~A2∨~A3

--that is, we can conclude only that at least one of the hypothesis or our starting
assumptions is false. Observation and logic will not tell us which one is false.

Crucial Experiments Impossible. Duhem argues that crucial
experiments are impossible in science. A crucial experiment is supposed to be an
experiment which will definitively decide between two alternative theories. The idea
seems to be that a crucial experiment enables us to make a disjunctive syllogism.
Suppose that we have two rival hypotheses, H1 and H2. Lumping
all our auxiliary assumptions into the single symbol A, we have, let us suppose:

1. H1∨ H2
2. (H1 &
A)
→ O1
3. (H2 &
A)
→ O2

and let us suppose that the observations predicted by the two hypotheses are mutually
incompatible, so that

4. O1↔ ~O2

Now we perform the crucial experiment. Suppose we find that O1. By 4, we
know that ~O2. So from this together with 3, we can conclude that ~(H2 & A). Of course, at this point we hit the problem of holism; all we know now is
that ~H2 or ~A, but we don't know which. However, suppose for the sake of
argument that we can in fact conclude that ~H2. Then from 1, we can conclude
that H1. The crucial experiment has validated H1 by ruling out H2.

At this point we reach Duhem's second criticism, namely that this form of argument only
works if we in fact know that 1, i.e. that one or the other of our two hypotheses is
correct. But we can never rule out the possibility that other hypotheses we haven't
thought of yet, incompatible with H1 and H2, are true. A disjunctive
syllogism works only if we know that we have exhausted the possibilities and then ruled
out all but one of them. But we can't ever be certain that we have found all the possible
hypotheses that might explain the evidence.

(Nonscientific example: In "Some Assembly Required," Buffy (the vampire
slayer) and friends are trying to figure out why a corpse is missing from the
cemetery, and dig up another grave to gather observational evidence. H1:
flesh-eating demon. H2: army of zombies. O1: grave with corpse. O2: grave
without corpse. Clearly condition 4 is satisfied. When they don't find a
corpse, they conclude that a voodoo practitioner is raising an army of
zombies. However, it turns out that 1 is false: the truth is a completely
different hypothesis, H3, namely that a science student has been gathering
parts to make a Frankenstein-style companion for his dead but reanimated
brother.)

Theories aren't directly induced from observational data. Duhem
criticizes Newton's idea that the law of gravity was "deduced" (he had in
mind some form of induction, not "deduction" as we understand it) from
observational claims. The background here is Newton's rejection of
"hypotheses" in science:

I have not as yet been able to discover the reason for these properties
of gravity from phenomena, and I do not feign hypotheses. For whatever is
not deduced from the phenomena must be called a hypothesis; and hypotheses,
whether metaphysical or physical, or based on occult qualities, or
mechanical, have no place in experimental philosophy. In this philosophy
particular propositions are inferred from the phenomena, and afterwards
rendered general by induction. (From Newton's Principia, trans.
I. Bernard Cohen and Anne Whitman. I've taken the quotation from the
Wikipedia article "Hypotheses non fingo.")

It is this view that Duhem is criticizing.

Humean Underdetermination (HUD): Laudan uses the term "Humean
Underdetermination" to refer to the view that for any observable evidence O, there is an indefinite number of hypotheses
which, together with auxiliary assumptions, logically imply O. One instance of
this is the familiar problem of fitting a curve to a set of points. There will
always be an infinite number of different curves that pass through any finite
set of points.

Laudan thinks all of these points (well, really he only addresses 1 and 4)
are correct and to some extent important, but that they do not have significant
relativistic consequences. These points concern deductive underdetermination. Relativists have concluded that, since logic doesn't compel
one theory choice over another, there must be a significant nonrational
component in theory choice.

But Laudan points out that to show this would require not merely deductive underdetermination, but
ampliative underdetermination. (An "ampliative inference" is one which
goes beyond what you could infer by means of deduction alone: for instance, an
inference from the evidence to claims about the future, or the distant past, or
things too small or far away to observe directly. If we use the term "induction"
broadly enough, an ampliative inference is just an inductive inference.) That is, what needs to be
shown is not that observation plus deduction will not determine theory choice,
but rather that "ampliative inference" will not determine a unique choice of
theory. Laudan argues that no one has in fact shown this.

On the other hand, Laudan doesn't say much about what ampliative principles
might cure underdetermination. It seems clear that deductive reasoning alone
will not narrow the range of acceptable theories to one. Goodman's puzzle
suggests that deductive reasoning plus enumerative induction (aka the straight
rule of induction, or the instantial model of induction) still leaves
significant underdetermination. What can fill the gap? That is, what principles
can we use to narrow down the choices between theories that are still left
standing by deduction and enumerative induction?

Proposed criteria have included: simplicity, fruitfulness, generality, etc.
(Duhem himself proposes "good sense" at the end of his article, though this
unfortunately seems somewhat vague!)

If all rational criteria still underdetermine theory choice, then it
seems that something else will need to fill the gap. This is where defenders of
an extreme sociological account of science have seen an opportunity: if reason
doesn't determine which theories to accept, then it will need to be supplemented
by social or psychological factors: individual bias, political commitments, and
the like.